Details

sample115.0ms

Algorithm

intervals

Results

31.0ms	84×	body	80	nan
25.0ms	36×	body	2560	valid
20.0ms	187×	body	80	valid
13.0ms	26×	body	1280	valid
5.0ms	12×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify483.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.0b	(fma (* a c) -4 (* b b))
1.0b	(- (sqrt (fma (* a c) -4 (* b b))) b)
23.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

30.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
9.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
69.0ms	(fma (* a c) -4 (* b b))
128.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
104.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify659.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
2	773
1	335
0	156

prune605.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.9b

localize58.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
2.8b	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.6b	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
23.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
101×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 166

Calls

4 calls:

13.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
36.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
28.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
3.0ms	(sqrt (fma (* a c) -4 (* b b)))

series875.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
307.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
297.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
144.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify876.0ms

Counts

178 → 178

Iterations

Iter	Nodes
done	2002
2	1434
1	557
0	246

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.2b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* a c) (* b b))
1.7b	(+ (sqrt (fma -4 (* a c) (* b b))) b)
14.4b	(/ (* (* a c) -4) a)
23.7b	(sqrt (fma -4 (* a c) (* b b)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
6×	`fma-def` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma -4 (* a c) (* b b))
11.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
42.0ms	(/ (* (* a c) -4) a)
3.0ms	(sqrt (fma -4 (* a c) (* b b)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma -4 (* a c) (* b b))
101.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
17.0ms	(/ (* (* a c) -4) a)
123.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify672.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	2000
2	976
1	292
0	121

prune476.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* -4 c) (+ (sqrt (fma -4 (* a c) (* b b))) b))
1.0b	(fma -4 (* a c) (* b b))
1.7b	(+ (sqrt (fma -4 (* a c) (* b b))) b)
23.7b	(sqrt (fma -4 (* a c) (* b b)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`fma-def` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `times-frac` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

27.0ms	(/ (* -4 c) (+ (sqrt (fma -4 (* a c) (* b b))) b))
0.0ms	(fma -4 (* a c) (* b b))
13.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
3.0ms	(sqrt (fma -4 (* a c) (* b b)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (* -4 c) (+ (sqrt (fma -4 (* a c) (* b b))) b))
97.0ms	(fma -4 (* a c) (* b b))
135.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
102.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify771.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
2	885
1	289
0	121

prune537.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.8b

regimes336.0ms

Accuracy

96.6% (0.6b remaining)

Error of 12.3b against oracle of 11.7b and baseline of 28.8b

bsearch320.0ms

Steps

Iters	Range		Point
7	1.9723660647371773e+81	3.4101289177416236e+83	3.2005525135011565e+83
12	-1.1055728218964216e-267	3.718336584209563e-309	-1.8410785388490295e-298

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample4.0s

Algorithm

intervals

Results

948.0ms	1103×	body	2560	valid
914.0ms	5761×	body	80	valid
650.0ms	957×	body	1280	valid
449.0ms	128×	body	160	valid
392.0ms	2981×	body	80	nan
216.0ms	480×	body	640	valid
96.0ms	115×	body	5120	valid
73.0ms	223×	body	320	valid